This is the html-rendered R markdown file (Rmd) which accompanies the manuscript:
Huber-Huber, C. & Melcher, D. (2020) The behavioural preview effect with faces results from predictive processing across the saccade. Manuscript submitted for publication.
The code used to generate this file reproduces all statistics and figures in the manuscript from the data which is provided as well. For all background information information about the study, however, please refer to the manuscript file.
Figure and table numbers correspond to figures and tables in the manuscript.
Here, we check the average performance across the experiment in the tilt discrimination task. Participants with less than 60% correct responses are excluded assuming that they did not do the task.
partnr Training prop.corr prop.corr<0.60
1: 33 Invalid 0.5191364 TRUE
2: 37 Invalid 0.5322266 TRUE
3: 8 Invalid 0.5430528 TRUE
4: 34 Valid 0.5475709 TRUE
5: 27 Invalid 0.5616438 TRUE
6: 40 Valid 0.5714286 TRUE
7: 18 Invalid 0.6050831 FALSE
8: 12 Invalid 0.6113744 FALSE
9: 19 Valid 0.6174168 FALSE
10: 36 Valid 0.6656863 FALSE
11: 25 Invalid 0.7247796 FALSE
12: 38 Valid 0.7431641 FALSE
13: 29 Invalid 0.7446184 FALSE
14: 22 Invalid 0.7497556 FALSE
15: 16 Invalid 0.7526882 FALSE
16: 15 Valid 0.7563601 FALSE
17: 32 Invalid 0.7608696 FALSE
18: 11 Valid 0.7617647 FALSE
19: 5 Valid 0.7626953 FALSE
20: 3 Invalid 0.7689282 FALSE
21: 17 Valid 0.7763672 FALSE
22: 2 Valid 0.7778865 FALSE
23: 6 Invalid 0.7864838 FALSE
24: 26 Valid 0.8164062 FALSE
25: 39 Invalid 0.8189824 FALSE
26: 9 Valid 0.8258317 FALSE
27: 24 Invalid 0.8406647 FALSE
28: 10 Invalid 0.8437500 FALSE
29: 7 Valid 0.8447266 FALSE
30: 13 Valid 0.8476562 FALSE
31: 28 Valid 0.8554688 FALSE
32: 35 Invalid 0.8563050 FALSE
33: 20 Invalid 0.8631476 FALSE
34: 21 Valid 0.8875855 FALSE
35: 31 Invalid 0.8895406 FALSE
36: 23 Valid 0.8935547 FALSE
37: 4 Invalid 0.8955665 FALSE
38: 41 Invalid 0.8970588 FALSE
39: 14 Invalid 0.9111328 FALSE
40: 30 Valid 0.9149560 FALSE
41: 1 Valid 0.9274510 FALSE
partnr Training prop.corr prop.corr<0.60
Thus, participants excluded are: 33, 37, 8, 34, 27, 40.
Number of participants per training group:
Training
Valid Invalid
17 18
Age:
Min. 1st Qu. Median Mean 3rd Qu. Max.
18.0 20.0 21.0 22.5 24.0 41.0
Gender (0 -> female; 1 -> male):
gender
0 1
25 10
Handedness (0 -> left; 1 -> right):
handedness
0 1
6 29
Eyedness (0 -> left; 1 -> right):
eyedness
0 1
14 21
For details on the model fitting and model comparison approach, see the corresponding Rmd source code file.
| Dependent variable: | |||||
| -1 / Response time [sec] | |||||
| Fitting method: | |||||
| REML | REML | REML | REML | ||
| (1) | (2) | (3) | (4) | ||
| Random effects variances | |||||
| Participant | |||||
| (Intercept) | 0.039 | 0.049 | 0.049 | 0.049 | |
| Target Orientation (In-Up) | 0.002 | 0.002 | 0.002 | ||
| Preview (Inv-Val) | 0.001 | 0.001 | 0.001 | ||
| Trial number | 0.010 | 0.010 | 0.010 | ||
| Target Orientation x Preview | 0.003 | 0.003 | 0.003 | ||
| Target Orientation x Trial number | 0.0001 | 0.0001 | 0.0001 | ||
| Preview x Trial number | 0 | 0 | |||
| Target Orientation x Preview x Trial number | 0 | ||||
| Residual Variance | 0.039 | 0.036 | 0.036 | 0.036 | |
| Fixed effects | |||||
| Target Orientation (In-Up) | 0.033 | 0.037 | 0.037 | 0.037 | |
| (0.007) | (0.010) | (0.010) | (0.010) | ||
| t = 4.675 | t = 3.749 | t = 3.749 | t = 3.749 | ||
| Preview (Inv-Val) | 0.044 | 0.041 | 0.041 | 0.041 | |
| (0.007) | (0.009) | (0.009) | (0.009) | ||
| t = 6.143 | t = 4.549 | t = 4.549 | t = 4.549 | ||
| Training (Inv-Val) | -0.144 | -0.138 | -0.138 | -0.138 | |
| (0.068) | (0.075) | (0.075) | (0.075) | ||
| t = -2.128 | t = -1.831 | t = -1.831 | t = -1.831 | ||
| Trial number | -0.074 | -0.077 | -0.077 | -0.077 | |
| (0.004) | (0.017) | (0.017) | (0.017) | ||
| t = -20.736 | t = -4.388 | t = -4.388 | t = -4.388 | ||
| Target Orientation x Preview | -0.010 | -0.014 | -0.014 | -0.014 | |
| (0.014) | (0.016) | (0.016) | (0.016) | ||
| t = -0.729 | t = -0.841 | t = -0.841 | t = -0.841 | ||
| Target Orientation x Training | 0.010 | 0.002 | 0.002 | 0.002 | |
| (0.014) | (0.020) | (0.020) | (0.020) | ||
| t = 0.696 | t = 0.083 | t = 0.083 | t = 0.083 | ||
| Preview x Training | -0.074 | -0.070 | -0.070 | -0.070 | |
| (0.014) | (0.018) | (0.018) | (0.018) | ||
| t = -5.242 | t = -3.848 | t = -3.848 | t = -3.848 | ||
| Target Orientation x Trial number | 0.016 | 0.013 | 0.013 | 0.013 | |
| (0.007) | (0.007) | (0.007) | (0.007) | ||
| t = 2.269 | t = 1.866 | t = 1.866 | t = 1.866 | ||
| Preview x Trial number | 0.001 | 0.003 | 0.003 | 0.003 | |
| (0.007) | (0.007) | (0.007) | (0.007) | ||
| t = 0.079 | t = 0.425 | t = 0.425 | t = 0.425 | ||
| Training x Trial number | 0.065 | 0.058 | 0.058 | 0.058 | |
| (0.007) | (0.035) | (0.035) | (0.035) | ||
| t = 9.151 | t = 1.676 | t = 1.676 | t = 1.676 | ||
| Target Orientation x Preview x Training | 0.015 | 0.010 | 0.010 | 0.010 | |
| (0.028) | (0.033) | (0.033) | (0.033) | ||
| t = 0.522 | t = 0.300 | t = 0.300 | t = 0.300 | ||
| Target Orientation x Preview x Trial number | 0.007 | 0.012 | 0.012 | 0.012 | |
| (0.014) | (0.014) | (0.014) | (0.014) | ||
| t = 0.486 | t = 0.854 | t = 0.854 | t = 0.854 | ||
| Target Orientation x Training x Trial number | -0.007 | -0.002 | -0.002 | -0.002 | |
| (0.014) | (0.014) | (0.014) | (0.014) | ||
| t = -0.469 | t = -0.122 | t = -0.122 | t = -0.122 | ||
| Preview x Training x Trial number | 0.033 | 0.028 | 0.028 | 0.028 | |
| (0.014) | (0.014) | (0.014) | (0.014) | ||
| t = 2.359 | t = 2.051 | t = 2.051 | t = 2.051 | ||
| Target Orientation x Preview x Training x Trial number | -0.015 | -0.017 | -0.017 | -0.017 | |
| (0.028) | (0.027) | (0.027) | (0.027) | ||
| t = -0.541 | t = -0.618 | t = -0.618 | t = -0.618 | ||
| Grand mean | -1.025 | -1.022 | -1.022 | -1.022 | |
| (0.034) | (0.038) | (0.038) | (0.038) | ||
| t = -30.344 | t = -27.213 | t = -27.213 | t = -27.213 | ||
| Observations | 12,671 | 12,671 | 12,671 | 12,671 | |
| AICc | -4852.342 | -5702.931 | -5700.924 | -5698.916 | |
| Log Likelihood | 2444.198 | 2874.509 | 2874.509 | 2874.509 | |
| Deviance | -4888.396 | -5749.019 | -5749.019 | -5749.019 | |
| Df | 18 | 23 | 24 | 25 | |
| χ2 | 860.623 | 0 | 0 | ||
| χ2 Df | 5 | 1 | 1 | ||
| p | < .001 | 1.000 | 1.000 | ||
| Model is singular | †| †| |||
The table of model comparisons above indicates that the model with the complete random effects structure is singular. Removing the random slope of the highest-order interaction with zero variance, still leads to a singular model. Removing the next zero variance component leads to a model that we call the maximum identifiable model (here Model 2). This model is better than the model without random slopes as can be seen from the model comparison indices in that table.
Figure 2. Estimated marginal means from the maximum identified model on response time data (Model 2). The preview effect, the difference between valid and invalid preview trials, depended on the training condition. In contrast to valid training, there was no evidence for a preview effect with invalid training (see also Models 2a and 2b below). Note that effect estimates were obtained for the first trial of the test phase. Error bars represent asymptotic confidence intervals.
Figure 3. Fixed effect coefficients of the maximum identified linear mixed model on response times (Model 2).
| Parameter | Estimate | Std. Error | t value | 2.5 % | 97.5 % |
| ((Intercept)) | -1.022 | 0.038 | -27.213 | -1.095 | -0.948 |
| Target Orientation (In-Up) | 0.037 | 0.010 | 3.749 | 0.018 | 0.056 |
| Preview (Inv-Val) | 0.041 | 0.009 | 4.549 | 0.024 | 0.059 |
| Training (Inv-Val) | -0.138 | 0.075 | -1.831 | -0.285 | 0.009 |
| Trial number | -0.077 | 0.017 | -4.388 | -0.111 | -0.042 |
| Target Orientation x Preview | -0.014 | 0.016 | -0.841 | -0.046 | 0.018 |
| Target Orientation x Training | 0.002 | 0.020 | 0.083 | -0.037 | 0.040 |
| Preview x Training | -0.070 | 0.018 | -3.848 | -0.105 | -0.034 |
| Target Orientation x Trial number | 0.013 | 0.007 | 1.866 | -0.001 | 0.027 |
| Preview x Trial number | 0.003 | 0.007 | 0.425 | -0.010 | 0.016 |
| Training x Trial number | 0.058 | 0.035 | 1.676 | -0.010 | 0.127 |
| Target Orientation x Preview x Training | 0.010 | 0.033 | 0.300 | -0.054 | 0.074 |
| Target Orientation x Preview x Trial number | 0.012 | 0.014 | 0.854 | -0.015 | 0.038 |
| Target Orientation x Training x Trial number | -0.002 | 0.014 | -0.122 | -0.029 | 0.026 |
| Preview x Training x Trial number | 0.028 | 0.014 | 2.051 | 0.001 | 0.055 |
| Target Orientation x Preview x Training x Trial number | -0.017 | 0.027 | -0.618 | -0.070 | 0.037 |
Figure 4. Response times showed an interaction of Training x Preview x Trial Number, which suggested that training with only valid trials resulted in a larger preview effect than training with only invalid trials particularly in the beginning of the test phase. The preview effect then evolved in opposite directions for both training groups. Compared to the invalid training group, the preview effect in the valid training group declined. Each dot is one trial. Trial number was standardized and centered on the first trial of the test phase.
Note, Figure 4 is zoomed-in at the y-axis. Only half of all individual trial data points (sampled randomly) are plotted in order to decrease the size of the plot.
Here we follow up the interaction Preview x Training x Trial Number to see whether the preview effects are significant within the training groups.
| Parameter | Estimate | Std. Error | t value | 2.5 % | 97.5 % |
| ((Intercept)) | -0.953 | 0.056 | -17.112 | -1.065 | -0.841 |
| Target Orientation (In-Up) | 0.036 | 0.013 | 2.799 | 0.011 | 0.061 |
| Preview (Inv-Val) | 0.076 | 0.015 | 5.154 | 0.047 | 0.105 |
| Trial number | -0.106 | 0.030 | -3.525 | -0.166 | -0.045 |
| Target Orientation x Preview | -0.019 | 0.024 | -0.800 | -0.067 | 0.028 |
| Target Orientation x Trial number | 0.014 | 0.009 | 1.524 | -0.004 | 0.032 |
| Preview x Trial number | -0.011 | 0.009 | -1.187 | -0.029 | 0.007 |
| Target Orientation x Preview x Trial number | 0.021 | 0.019 | 1.124 | -0.016 | 0.057 |
| Parameter | Estimate | Std. Error | t value | 2.5 % | 97.5 % |
| ((Intercept)) | -1.091 | 0.051 | -21.520 | -1.193 | -0.989 |
| Target Orientation (In-Up) | 0.038 | 0.015 | 2.563 | 0.009 | 0.067 |
| Preview (Inv-Val) | 0.007 | 0.011 | 0.607 | -0.015 | 0.028 |
| Trial number | -0.047 | 0.019 | -2.535 | -0.084 | -0.010 |
| Target Orientation x Preview | -0.007 | 0.022 | -0.316 | -0.051 | 0.036 |
| Target Orientation x Trial number | 0.012 | 0.011 | 1.053 | -0.011 | 0.034 |
| Preview x Trial number | 0.017 | 0.010 | 1.676 | -0.003 | 0.036 |
| Target Orientation x Preview x Trial number | 0.002 | 0.020 | 0.118 | -0.037 | 0.041 |
The Preview x Training x Trial Number interaction is significant. Note that in the figure illustrating this interaction, the preview effect is the difference between dashed (invalid preview) and solid (valid preview) lines in the direction of the y-axis. If the training phase was valid, there is a preview effect in the beginning of the following test phase which decreases in the course of the test phase. If training phase was invalid, there is a smaller/no preview effect in the beginning of the following test phase which then, compared to the valid training condition, tends to increase. In other words, the influence of training equals across time.
Besides this interaction, there is a significant main effect of Target Orientation. This effect is in the expected direction known from previous research, i.e. faster responses with upright than with inverted targets. The direction of the effect can be seen from the contrasts of the Target Orientation factor and the value of the effect estimate. The contrast is In-Up, meaning inverted minus upright. That means the effect estimate is calculated by subtracing upright target trials from inverted target trials. That means positive values indicate larger dependent variable values for inverted than for upright targets. The dependent variable transformation of -1 / RT before model fitting ensured that larger values still mean slower responses (i.e. maintain the direction of the effect). Thus, given a positive value for the Target Orientation effect estimate () and confidence intervals excluding zero, we can conclude that responses were significanly faster with upright than with inverted targets.
For details on the model fitting and model comparison approach, see the corresponding Rmd source code file.
| Dependent variable: | ||||
| Task error (log odds) | ||||
| (5) | (6) | (7) | (8) | |
| Random effects variances | ||||
| Participant | ||||
| (Intercept) | 0.344 | 0.340 | 0.340 | 0.340 |
| Target Orientation (In-Up) | 0.134 | 0.134 | 0.134 | |
| Preview (Inv-Val) | 0.027 | 0.027 | 0.027 | |
| Trial number | 0.032 | 0.032 | 0.032 | |
| Target Orientation x Trial number | 0.043 | 0.043 | 0.043 | |
| Target Orientation x Preview x Trial number | 0.136 | 0.136 | 0.136 | |
| Preview x Trial number | 0 | 0 | ||
| Target Orientation x Preview | 0 | |||
| Residual Variance | 1 | 1 | 1 | 1 |
| Fixed effects | ||||
| Target Orientation (In-Up) | 0.655 | 0.676 | 0.676 | 0.676 |
| (0.085) | (0.107) | (0.107) | (0.107) | |
| t = 7.725 | t = 6.331 | t = 6.331 | t = 6.331 | |
| Preview (Inv-Val) | -0.107 | -0.101 | -0.101 | -0.101 |
| (0.085) | (0.090) | (0.090) | (0.090) | |
| t = -1.265 | t = -1.125 | t = -1.125 | t = -1.125 | |
| Training (Inv-Val) | 0.082 | 0.070 | 0.070 | 0.070 |
| (0.216) | (0.216) | (0.216) | (0.216) | |
| t = 0.381 | t = 0.326 | t = 0.326 | t = 0.326 | |
| Trial number | 0.020 | -0.003 | -0.003 | -0.003 |
| (0.042) | (0.054) | (0.054) | (0.054) | |
| t = 0.463 | t = -0.048 | t = -0.048 | t = -0.048 | |
| Target Orientation x Preview | 0.028 | 0.027 | 0.027 | 0.027 |
| (0.169) | (0.170) | (0.170) | (0.170) | |
| t = 0.166 | t = 0.158 | t = 0.158 | t = 0.158 | |
| Target Orientation x Training | -0.045 | -0.009 | -0.009 | -0.009 |
| (0.170) | (0.213) | (0.213) | (0.213) | |
| t = -0.265 | t = -0.043 | t = -0.043 | t = -0.043 | |
| Preview x Training | -0.156 | -0.160 | -0.160 | -0.160 |
| (0.169) | (0.179) | (0.179) | (0.179) | |
| t = -0.921 | t = -0.892 | t = -0.892 | t = -0.892 | |
| Target Orientation x Trial number | -0.199 | -0.177 | -0.177 | -0.177 |
| (0.084) | (0.093) | (0.093) | (0.093) | |
| t = -2.363 | t = -1.893 | t = -1.893 | t = -1.893 | |
| Preview x Trial number | -0.023 | -0.031 | -0.031 | -0.031 |
| (0.084) | (0.085) | (0.085) | (0.085) | |
| t = -0.267 | t = -0.370 | t = -0.370 | t = -0.370 | |
| Training x Trial number | -0.115 | -0.111 | -0.111 | -0.111 |
| (0.084) | (0.106) | (0.106) | (0.106) | |
| t = -1.363 | t = -1.053 | t = -1.053 | t = -1.053 | |
| Target Orientation x Preview x Training | -0.071 | -0.068 | -0.068 | -0.068 |
| (0.339) | (0.340) | (0.340) | (0.340) | |
| t = -0.210 | t = -0.200 | t = -0.200 | t = -0.200 | |
| Target Orientation x Preview x Trial number | -0.057 | -0.071 | -0.071 | -0.071 |
| (0.169) | (0.182) | (0.182) | (0.182) | |
| t = -0.338 | t = -0.391 | t = -0.391 | t = -0.391 | |
| Target Orientation x Training x Trial number | 0.006 | 0.033 | 0.033 | 0.033 |
| (0.169) | (0.186) | (0.186) | (0.186) | |
| t = 0.034 | t = 0.178 | t = 0.178 | t = 0.178 | |
| Preview x Training x Trial number | 0.027 | 0.022 | 0.022 | 0.022 |
| (0.169) | (0.170) | (0.170) | (0.170) | |
| t = 0.160 | t = 0.127 | t = 0.127 | t = 0.127 | |
| Target Orientation x Preview x Training x Trial number | 0.088 | 0.105 | 0.105 | 0.105 |
| (0.337) | (0.363) | (0.363) | (0.363) | |
| t = 0.261 | t = 0.288 | t = 0.288 | t = 0.288 | |
| Grand mean | -1.538 | -1.543 | -1.543 | -1.543 |
| (0.108) | (0.108) | (0.108) | (0.108) | |
| t = -14.216 | t = -14.257 | t = -14.257 | t = -14.257 | |
| Observations | 15,765 | 15,765 | 15,765 | 15,765 |
| AICc | 14817.779 | 14775.659 | 14777.665 | 14779.671 |
| Log Likelihood | -7391.87 | -7365.797 | -7365.797 | -7365.797 |
| Deviance | 14783.741 | 14731.595 | 14731.595 | 14731.595 |
| Df | 17 | 22 | 23 | 24 |
| χ2 | 52.146 | 0 | 0 | |
| χ2 Df | 5 | 1 | 1 | |
| p | < .001 | 1.000 | 1.000 | |
| Model is singular | †| †| ||
The table of model comparisons above indicates that the model with the complete random effects structure is singular. Removing the random slope of the less interesting component with zero variance, still leads to a singular model. Removing the next zero variance component leads to the maximum identifiable model (Model 6). This model is better than the model without random slopes as can be seen from the model comparison indices in the table above.
Figure 5. Fixed effect coefficients of the maximum identified generalized linear model on task errors (Model 6).
| Parameter | Estimate | 2.5 % | 97.5 % |
| ((Intercept)) | -1.543 | -1.762 | -1.328 |
| Target Orientation (In-Up) | 0.676 | 0.467 | 0.890 |
| Preview (Inv-Val) | -0.101 | -0.278 | 0.076 |
| Training (Inv-Val) | 0.070 | -0.363 | 0.503 |
| Trial number | -0.003 | -0.114 | 0.102 |
| Target Orientation x Preview | 0.027 | -0.307 | 0.361 |
| Target Orientation x Training | -0.009 | -0.429 | 0.416 |
| Preview x Training | -0.160 | -0.513 | 0.193 |
| Target Orientation x Trial number | -0.177 | -0.359 | 0.012 |
| Preview x Trial number | -0.031 | -0.198 | 0.135 |
| Training x Trial number | -0.111 | -0.325 | 0.102 |
| Target Orientation x Preview x Training | -0.068 | -0.735 | 0.599 |
| Target Orientation x Preview x Trial number | -0.071 | -0.431 | 0.285 |
| Target Orientation x Training x Trial number | 0.033 | -0.331 | 0.405 |
| Preview x Training x Trial number | 0.022 | -0.312 | 0.355 |
| Target Orientation x Preview x Training x Trial number | 0.105 | -0.610 | 0.820 |
Additional figure illustrating the Target Orientation x Trial Number interaction which is strictly speaking not significant and anyway theoretically not relevant.
Clearly less task error with upright than with inverted targets. In addition, there is a borderline significant Target Orientation x Trial Number interaction in the direction of a decreasing target orientation effect (inverted minus upright) across the test phase. However, strickly speaking, this effect is not significant and it is theoretically not relevant, so we do not interpret it and do not mention it in the paper.
Training influenced the preview effect in response times. In the beginning of the test phase, there was a clear preview effect if participants had trained with only valid trials. However, after invalid training there was no evidence for a preview effect. Moreover, this change in the preview effect equalled during the test phase.
In addition but theoretically not relevant, target face orientation, affected performance leading to slower responses and more errors when target faces were inverted compared to when they were upright.
R version 3.6.1 (2019-07-05)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Sierra 10.12.6
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
locale:
[1] C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] knitr_1.24 citr_0.3.2 stargazer_5.2.2 boot_1.3-23 emmeans_1.4.5 lme4_1.1-21 Matrix_1.2-17 ggplot2_3.2.1
[9] data.table_1.12.2
loaded via a namespace (and not attached):
[1] gtools_3.8.1 tidyselect_0.2.5 xfun_0.9 reshape2_1.4.3 purrr_0.3.2 splines_3.6.1 lattice_0.20-38 colorspace_1.4-1
[9] miniUI_0.1.1.1 htmltools_0.3.6 yaml_2.2.0 rlang_0.4.0 pillar_1.4.2 nloptr_1.2.1 later_0.8.0 glue_1.3.1
[17] withr_2.1.2 plyr_1.8.4 stringr_1.4.0 munsell_0.5.0 gtable_0.3.0 mvtnorm_1.0-11 coda_0.19-3 evaluate_0.14
[25] labeling_0.3 httpuv_1.5.1 highr_0.8 Rcpp_1.0.2 xtable_1.8-4 scales_1.0.0 promises_1.0.1 mime_0.7
[33] digest_0.6.20 stringi_1.4.3 dplyr_0.8.3 shiny_1.3.2 grid_3.6.1 tools_3.6.1 magrittr_1.5 lazyeval_0.2.2
[41] tibble_2.1.3 crayon_1.3.4 pkgconfig_2.0.2 MASS_7.3-51.4 estimability_1.3 assertthat_0.2.1 minqa_1.2.4 rmarkdown_1.15
[49] rstudioapi_0.10 R6_2.4.0 nlme_3.1-140 compiler_3.6.1